In general, various types of recording and reproduction apparatuses are designed to reduce the error rate of reproduced data by coding data to be recorded and recording the data. During the reproduction of the recording and reproduction apparatus, after a reproduced waveform read from a recording medium is equalized to a target equalized characteristic, this is converted into a digital equalized signal, and furthermore, after the signal is converted into coded data, it is decoded, thereby reconstructing the original data.
Similarly, also, in various communication devices, by coding data to be communicated and transmitting it, the error rate of received data is reduced. During the reception by the communication device, after the received waveform is equalized to a target equalized characteristic, it is converted into a digital equalized signal, and furthermore, the signal is converted into coded data, and then it is decoded, thereby reconstructing the original data.
For conversion from a digital equalized signal into coded data during the reproduction of the above-described recording and reproduction apparatus and the reception of the above-described communication device, a viterbi decoding technique, which is one of the maximum likelihood detection methods, is often used.
In an ordinary viterbi decoding technique, by denoting a reproduced signal containing noise at time k as yk, an ideal signal with no noise in a state s on a Trellis diagram as dk(s), a logarithmic likelihood, that is, a metric mk(s), is calculated on the basis of the following equation (1):mk(s)=mk−1(s′)+{yk−dk(s)}2  (1)
where s′ is the state at the previous time k−1 of an input path on the Trellis diagram.
In the viterbi decoding technique, by selecting the path whose metric calculated using equation (1) in each state on the Trellis diagram is smaller, the detection of the maximum likelihood path is performed.
Alternatively, the detection of the maximum likelihood path may be performed in such a way that the branch metric in equation (1), that is, the second term {yk−dk(s)}2 of the right side is subtracted from mk−1(s′) and the path whose metric is greater is selected.
For the metric, eventually, only the magnitude relationship is important. Therefore, usually, the metric mk(s) is computed in such a way that a predetermined appropriate constant is subjected to the four basic operations of arithmetic: addition, subtraction, multiplication, and division in the right side of equation (1), and is normalized into as simple an equation as possible.
The normalization of equation (1) will now be described specifically. When equation (1) is expanded, the result is as shown in the following equation (2):mk(s)=mk−1(s′)+yk2−2ykdk(s)+dk(s)2  (2)
When yk2 is subtracted from equation (2) and the result is divided by 2, the following equation (3) is obtained:mk(s)=mk−1(s′)+dk(s){dk(s)/2−yk}  (3)
However, although the value of the metric mk(s) of the left side of equation (3) differs from that of the metric mk(s) of the left side of equation (2), the same symbol is used as the normalized metric.
Next, a method of calculating the metric mk(s) by applying the normalized equation (3) will now be described by using as an example a case in which a three-valued detection is performed by using a partial response class 1 (PR1) equalizing method, a partial response class 4 (PR4) equalizing method, etc.
The partial response class 1 equalizing method is an equalizing method employed in 3.8-mm and 8-mm tape streamer magnetic recording and reproduction apparatus, etc., and is known to have a characteristic for suppressing noise in a high-frequency band of a reproduced signal. The partial response class 4 equalizing method is an equalizing method employed in a hard disk drive, a consumer-oriented digital VCR (Video Cassette Recorder), etc., and is known to have a characteristic for suppressing noise in two bands, a low-frequency band containing DC components of a reproduced signal and a high-frequency band.
When a three-valued detection is to be performed, a normalized detected voltage dk(s) is of three types of {−1, 0, +1}, but in practice, the reproduced signal is quantized. Therefore, if the absolute value of the average detected voltage is denoted as V, the normalized detected voltage dk(s) is represented as {−V, 0, +V}.
In this case, the branch metric dk(s) {dk(s)/2−yk} of equation (3) is limited to the following equations. (4-1) to (4-3).
In the case of dk(s)=+V,V(V/2−yk)  (4-1)
In the case of dk(s)=0,0  (4-2)
In the case of dk(s)=−VV(V/2+yk)  (4-3)
Furthermore, each of equations (4-1) to (4-3) is divided by V, and each branch metric is normalized as shown in the following equations (5-1) to (5-3).
In the case of dk(s)=+V,V/2−yk  (5-1)
In the case of dk(s)=00  (5-2)
In the case of dk(s)=−VV/2+yk  (5-3)
If the branch metric is calculated using the equations (5-1) to (5-3), the multiplier of the circuit for calculating the branch metric can be omitted when compared to a case in which the branch metric is calculated using the equations (5-1) to (5-3).
Next, a description will now be given of compensation in a case where a non-linear upper and lower asymmetry is observed in a reproduced waveform during the reproduction of the above-described recording and reproduction apparatus. Such non-linear upper and lower asymmetry of a reproduced waveform is caused by a magnetic configuration of a recording and reproduction head mounted in the recording and reproduction apparatus.
For example, in a case where there is an asymmetry of magnetic domains in the head core of an inductive reproduction head, or in a case where the magnetoresistance element of a magnetoresistance reproduction head has an inappropriate bias magnetic-field intensity, there are cases in which a conspicuous upper and lower asymmetry is observed in the reproduced waveform.
When an upper and lower asymmetry is observed in the reproduced waveform, unless some countermeasures are taken, the error correction rate during decoding is decreased. Therefore, usually, some kind of asymmetry correction is performed. Asymmetry correction can be performed when a recorded code is converted into a recording rectangular waveform during recording or when a reproduced waveform is equalized in an analog manner during reproduction.
On the other hand, a method is conceived in which non-linear components due to the upper and lower asymmetry of the reproduced waveform are compensated for when the digital equalized signal is converted into coded data during reproduction.
For example, when a three-valued detection is to be performed, if the absolute value of the negative detected voltage is denoted as U and the normalized detected voltage dk(s) is represented as {−U, 0, +V}, the branch metric dk(s){dk(s)/2−yk} of equation (3) is limited to the following equations (6-1) to (6-3).
In the case of dk(s)=+V,V(V/2−yk)  (6-1)
In the case of dk(s)=00  (6-2)
In the case of dk(s)=−UU(U/2+yk)  (6-3)
When the branch metrics are computed using the equations (6-1) to (6-3), a computation of multiplying V or U is required.
Furthermore, if equations (6-1) to (6-3) are normalized by being divided by V similarly to that in which equations (4-1) to (4-3) and equations (5-1) to (5-3) are normalized, the following equations (7-1) to (7-3) are obtained.
In the case of dk(s)=+V,V/2−yk  (7-1)
In the case of dk(s)=00  (7-2)
In the case of dk(s)=−U(U/V)(U/2+yk)  (7-3)
However, even if the branch metrics are computed using the normalized equations (7-1) to (7-3), division and multiplication operations are necessary.
When division and multiplication operations are performed in the calculation of the metric, since a multiplier and a divider are necessary for the computation circuit, problems arise in that the circuit scale becomes larger and the computation time is increased correspondingly.
Therefore, in the non-linear compensation in the calculation of the metric, a method which does not require the above-described multiplication has been proposed.
For example, in L. Fredrickson, G. Betti, M. Marrow, G. Maguire and P. Gillen, “Trellis Coding in the Venus PRML Read/Write Channel,” IEEE Trans. on Magn., vol. 33, no. 5, pp. 2743-2745, September 1997 (hereinafter referred to as “reference 1”), by approximating U/V to 1, a method of using the following equations (8-1) to (8-3) instead of equations (7-1) to (7-3) is described.
In the case of dk(s)=+V,V/2−yk  (8-1)
In the case of dk(s)=00  (8-2)
In the case of dk(s)=−UU/2+yk  (8-3)
In the method described in reference 1, the absolute value U of the negative detected voltage in equation (8-3) is given by the register setting of the computation circuit.
According to the method described in reference 1, since there is no need to execute multiplication and division operations in the calculation of the metric, an increase in the scale of the computation circuit can be suppressed, and the computation time can be shortened.
However, in the method described in reference 1, since an approximation with U/V=1 is used in the calculation of the metric, there is a problem in that the accuracy of the calculation result is low.
Therefore, there has been a demand for the realization of a metric calculation method in which an approximation is not used and a multiplier is not used. However, conventionally, there is a problem in that such a method has not been invented.